Show A_n contains every 3-cycle if n >= 3; show A_n is generated by 3-
cycles for n >= 3; let r and s be fixed elements of {1, 2,..., n} for n
>= 3 and show that A_n is generated by the n 'special' 3-cycles of the
form (r, s, i) for 1 <= i <= n.

Demonstrate that in the (n!) permutation of the first n integers in a
table of dimension n! rows and n columns, the arithmetic mean of the
squares of each column terms is equal to (n+1)(4n+2)/12, and the
arithmetic mean of the crossproduct between any two columns is equal
to (n+1)(3n+2)/12.

Someone is trying to remember a phone number but cannot remember the
whole thing. He remembers 279-XXXX and that the last 4 numbers must
contain a 2 and a 7 and a 9. He only has 2, 7, or 9 as digits. How
many possible completions are there?